Estimating the contribution of infrastructure to national productivity in Europe

Transcription

1 Thoung et al. Infrastructure Complexity (2015) 2:5 DOI /s RESEARCH Estimating the contribution of infrastructure to national productivity in Europe Chris Thoung 1, Peter Tyler 2* and Rachel Beaven 3 Open Access Abstract While there is much interest in understanding the contribution that investment in different types of infrastructure can make to the economic development of cities, regions and nations, such research is constrained by various methodological difficulties. Following the approach of Égert, Kozluk and Sutherland (2009), this paper seeks to identify whether countries might be over- or under-investing in infrastructure relative to other forms of capital investment, from the point of view of raising productivity. While subject to various limitations (and also highlighting the continuing data constraints in this area), such an analysis provides a consistent and comparable basis on which to assess whether countries might benefit from additional infrastructure investment or, conversely, whether they might in fact stand to gain from alternative forms of fixed capital formation. The article analyses five types of infrastructure in the 27 Member States of the European Union (prior to 2013), Norway and Switzerland. We find some evidence of over-investment in electricity-generation capacity (investment in other forms of capital would likely yield higher productivity returns) and under-investment in roads, motorways and telephone infrastructure (there is potential for greater productivity growth from investing in these infrastructures). The evidence of a relationship between rail investment and productivity is less clear. While the results suggest that countries might stand to improve their national productivity by shifting the balance between infrastructure and other capital, higher productivity is not a country s only objective. Resilient infrastructure provision and/or upgrades with a view to pursuing other objectives such as climate-change mitigation may take precedence, necessitating at least some degree of non-optimal investment. Keywords: Infrastructure; Investment; Growth; Eurostat Background There is much interest by policy makers in understanding how investment in infrastructure can influence economic growth (Aschauer 1989, Esfahani and Ramírez 2003, Calderón and Servén 2004, Canning and Pedroni 2004, Romp and de Haan, 2005, Égert et al. 2009, Sahoo, et al. 2010). In the United Kingdom for example, HM Treasury commented recently that Infrastructure forms the economic backbone of the UK. It is the fabric that defines us as a modern industrialised nation. The standard and resilience of infrastructure in the UK has a direct relationship to the growth and competitiveness of our economy, our quality of life and our ability to meet * Correspondence: 2 Department of Land Economy, University of Cambridge, Cambridge, UK Full list of author information is available at the end of the article our climate change objectives and commitments (HM Treasury, 2010). Whilst it is clear that investment in infrastructure (often referred to as public capital) is essential to stimulate economic growth much remains unknown about the size of the contribution it can make and how this varies by type of infrastructure. As Romp and de Haan (2005) remarked in their extensive review article the issue had received only scant attention at that time, although they did present findings from some fifty studies. They also cited Holz-Eakin and Lovely s earlier observation that a somewhat surprising feature of the existing literature was the noticeable absence of formal economic models of the productivity effects of infrastructure (1996, p 106). The relative paucity of research in this important area must partly reflect the conceptual and measurement 2015 Thoung et al. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly credited.

2 Thoung et al. Infrastructure Complexity (2015) 2:5 Page 2 of 22 problems associated with identifying the relationship between economic growth and infrastructure. The problems were extensively reviewed by Romp and de Haan (2005). They suggested that perhaps the most important concern is the direction of causality between public capital and aggregate output: while public capital may affect productivity and output, economic growth can also shape the demand and supply of public capital services, which is likely to cause an upward bias in the estimated returns to public capital if endogeneity is not addressed (p 42). Romp and de Haan (2005) also drew attention to the problems of defining and measuring infrastructure, including the advantages of physical measures. The econometric issues posed in relation to causality have recently been examined by Pradhan and Bagchi (2013) in their assessment of the effects of transportation infrastructure on economic growth in India. They find evidence using a Vector Error Correction Model for bidirectional causality between road transportation and economic growth and unidirectional causality from rail transportation to economic growth. They highlight the importance of investment in these infrastructures on the growth of the Indian economy. Other research has also pointed to the problems of establishing what might be considered an optimal level of investment expenditure in new infrastructure and how this compares to the actual level. (Romp and de Haan, 2005, Hulten, 1996 and Canning and Pedroni 2004). There is also an emerging body of research on the relationship between investment in broadband infrastructure and economic growth (Czernich et al., 2011, Koutroumpis, 2009, and Tranos, 2012). This article investigates the contribution that investment in different types of infrastructure can make to the growth of productivity relative to other forms of gross fixed capital formation (investment) using, where possible, physical indicators of the infrastructure stock. In principle the approach outlined can also be used for cities and regions for which the appropriate data exists. To illustrate the basic approach we have used data from Eurostat for the 27 Member States of the European Union (prior to Croatia s accession in 2013), Norway and Switzerland. The analysis follows the time-series approach of Égert et al. (2009), applied in a European, rather than OECD context. The results highlight interesting patterns of European investment in infrastructure across countries relative to some notion of the optimal level of investment vis-à-vis productivity growth. In particular, these results suggest over-investment in electricity and under-investment in roads, motorways and telephones. The application of this approach also reveals the challenges presented by inadequate data, particularly when only short time series exist. The next section reviews the recent literature and highlights key research challenges. Past analyses of the economic contribution of infrastructure Our concern is to investigate the relationship between investment in infrastructure and the growth of productivity. The standard approach is to adopt a standard neoclassical production function augmented by infrastructure as a separate growth factor with additional explanatory variables to either decompose the effects of existing inputs on production (e.g., education rates to proxy human capital) or introduce other, perhaps more institutional, factors (e.g., proxies for political stability, internal market competitiveness or trade openness). The literature is substantial and Levine and Renelt (1992) state that over 50 variables have been found to be significantly correlated with growth in at least one regression (page 942). This was the approach adopted byégertetal.(2009)intheiranalysis..theysoughtto identify the contribution of infrastructure investment to economic growth relative to conventional investment. The key types of infrastructure investigated in their research were roads (with motorways identified separately), rail, electricity and telephones. The research used a theoretical framework based on Mankiw et al. (1992). The growth model was a Cobb-Douglas production function with decreasing returns to capital and the estimation work is based on a heterogeneous, fixedeffects cross-country panel framework that adopted an Engle and Granger (1987) two-step error-correction model approach. The data comprised subsets of OECD countries over the period , although the time span by individual country varied greatly (as few as 16 observations in some cases). The work highlighted the nature of the conceptual and empirical problems that arise. The measurement of capital is a classic empirical (as well as theoretical) problem in economics, with the Perpetual Inventory Method (PIM) being the most popular estimation method. This method models the capital stock as the accumulation of past investments (added to an assumed initial stock), adjusted for assumed depreciation and/or scrappage. Such estimates are sensitive to the underlying assumptions and, while PIMderived measures are commonplace, they are hardly ideal as proxies for the capital stock. Nevertheless, such data are often sectorally disaggregated, allowing for the identification of individual asset types. Aschauer (1989), for example, makes use of disaggregated economic data to separate capital into its respective components. In the case of infrastructure, an alternative indicator is of course a physical indicator such as road length or electricity-generation capacity. Such assets are easily-

3 Thoung et al. Infrastructure Complexity (2015) 2:5 Page 3 of 22 identified tangible assets, with the information readily available (although the availability of historical time series varies). However, even so, there is little in the way of information about infrastructure quality or its location. The quality of the infrastructure is clearly a factor in its potential contribution to the economy. The main contribution of Égert et al. (2009) framework is to identify how the contribution of infrastructure investment compares to other forms of investment i.e., whether there might be evidence of over- or under-investment in infrastructure in some countries. In this context, over-investment suggests that a country is utilising its infrastructure inefficiently and resources may in fact be better spent on other forms of capital that yield greater returns in terms of economic growth. Investment in energy provision was found to haveapositiveandsignificantimpactformostcountries investigated. There were also positive effects for road investment in some countries but not all. Positive effects were also found for rail investment in most countries. There was a rather mixed position in relation to investment in telecommunications. Canning and Pedroni (2004) assessed the long-run impact of infrastructure provision on per-capita income using the Penn World Tables that provide data for some 189 countries (Summers and Heston, 1991). They used data based on physical measures of infrastructure on an annual basis that included kilometres of paved road, electricity generating capacity and telephones per capita. Panel based estimations suggested that in the majority of cases infrastructure did make a contribution to long-term growth, albeit with considerable variations between countries. A key concern was to understand more about whether the amount of infrastructure provided was such that it was at a growth-maximising level and this was shown to be the case although again with a great deal of country variation. Their work helped to explain why there may appear contradictory results between models using cross-sectional rather than timeseries approaches. More recently, Sahoo et al. (2010) have assessed the effects of infrastructure investment on economic growth in China. Recognising that results have varied depending on whether measures of infrastructure are defined by investment expenditure or physical measures they developed a composite index of infrastructure using principal component analysis based on per-capita energy consumption, per-capita energy use, telephone lines per 1000 population, rail density per 1000 population, airtransport freight tons per kilometre and paved road as a proportion of total roads. Their research found that investment in infrastructure made a significant contribution to economic growth in China and they concluded that there is unidirectional causality from infrastructure development to output growth justifying China s high spending on infrastructure development since the early nineties (Sahoo, et al., 2010). In their analysis, Levine and Renelt (1992) find investment (a proxy for capital) to be robustly correlated with economic growth in the sense that the associated coefficients do not change sign and they remain statistically significant when the set of conditioning variables change (indicators of political stability/country type etc.). Capital is an important contributor to economic growth. It seems reasonable to suggest that without some basic level of infrastructure provision economic growth is likely to be constrained. However, beyond that point, whether infrastructure enables further growth or economic growth leads to increased infrastructure is difficult to disentangle in statistical terms. Many of the theoretical frameworks implicitly assume that the effect is in one direction: from investment through to economic growth because they include it as an input to production. This remains the case in the analysis that follows. Methods The approach in this article applies a simple exogenousgrowth model that incorporates infrastructure as an additional factor of production. In this way, it is possible to identify the contribution of infrastructure investment to national productivity in Europe, on a consistent and comparable basis. This section first sets out the theoretical model, before describing the estimation approach. It then goes on to discuss the interpretation of the results from such a model. Theoretical model The underlying exogenous-growth model is based on that of Mankiw et al. (1992), which explains output as a function of physical capital (K), human capital (H) and labour (L), with technology (A) as the residual. Y t ¼ FK ð t ; H t ; A t ; L t Þ From there, Mankiw et al. (1992) go on to derive their final human capital-augmented specification, to explain output per capita (i.e., productivity) as follows: lnð Y t Þ¼lnðA 0 Þþgt þ α L t 1 α lnðsk t Þ α 1 α ln ð n t þ g þ δþþ β 1 α ln ð h tþ Where: Y/L denotes GDP per capita A 0 is the starting level of technology

4 Thoung et al. Infrastructure Complexity (2015) 2:5 Page 4 of 22 g is the change in technology s K is the share of investment in output n is the change in labour/population δ is the rate of depreciation h is human capital t is a time index Égert et al. (2009) derive a similar specification, but with a variable for infrastructure per capita (inf) in place of Mankiw et al. (1992) use of human capital: lnð Y t Þ¼lnðA 0 Þþgt þ α L t 1 α lnðsk t Þ α 1 α ln ð n t þ g þ δþ þ β 1 α ln ð inf tþ It is this model that forms the basis of the regression analysis in this article. The subsequent decisions regarding the estimation approach are dictated by the data. Estimation approach Owing to the varying data availability across countries over time, as well as the heterogeneity observed in the infrastructure relationships across countries, it was not possible to apply an explicit panel-estimation approach. Instead, the analysis comprises a set of single-equation time-series analyses, one for each country and infrastructure type. The error-correction model adopted posits a long-run, cointegrating, equilibrium relationship between the variables expressed in levels, but the model also includes a dynamic part to the equation both to account for fluctuations in the short run but also for the adjustment process by which the system tends to correct to the long-run relationship. We adopt the Engle-Granger twostep approach to estimate these equations. In the first step of the Engle-Granger procedure, we estimated the long-term equilibrium as a cointegrating relationship between GDP per capita and its explanatory variables. This is known as the levels or long-run equation: y t ¼ β 0 þ β 1 s K t þ β 2 Δpop t þ β 3 time þ β 4 inf t where: y denotes (the natural logarithm of) GDP per capita s K is the share of investment in output (in natural logarithms) Δpop is the first difference of (the natural logarithm) of population time is a time trend (centred on 2005) inf it is the natural logarithm of infrastructure per capita indicator β 0, β 1, β 2, β 3 and β 4 are coefficients to be estimated, with the parameter on infrastructure, β 4, of primary interest An important specification test of the above equation is of stationarity in the resulting residuals, indicating the presence of a cointegrating relationship between the dependent and independent variables. This test consists of a unit-root (Augmented Dickey- Fuller) test on the residuals, under the null hypothesis that there is a unit root in the residuals (i.e., no cointegration). The absence of cointegration would mean that the equation is mis-specified and risks yielding a spurious regression with apparently (but not actually) statistically-significant results. The second step of the procedure estimated a dynamic equation, using one-period differences of the variables, to give the differences or short-run equation. This second equation included the lagged residuals from the long-run equation (which represented the deviations from the long-run equilibrium in each year), in order to model the adjustment mechanism by which deviations in per-capita output from that implied by the long-run relationships were corrected for (provided there was such a mechanism): Δy t ¼ β 5 þ β 6 Δs K t þ β 7 ΔΔpop t þ β 8 Δinf t þ β 9 ECM t 1 þ Σ J j¼1 β 10ðt jþ Δy t j where: y denotes (the natural logarithm of) GDP per capita s K is the share of investment in output (in natural logarithms) Δpop is the first difference of (the natural logarithm) of population inf it is the natural logarithm of infrastructure per capita indicator ECM is the one-period lag on the difference between the actual level of GDP per capita and that implied by the long-run equilibrium relationship above, in natural logarithms Δ is the difference operator β 5, β 6, β 7, β 8, β 9 and β 10 (t-j) are coefficients to be estimated, with the parameter on the long-run deviation, β 9, of primary interest, to test for stability The value of the lag length J was chosen to include as many lags of the dependent variable as were required to remove serial correlation from the shortrun residuals (as judged by a Breusch-Godfrey test at the 5 % level). In the vast majority of cases, one lag was sufficient, with two lags included in some cases. A minority of equations required more lags than that and, typically, could not be estimated at any reasonable lag length

5 Thoung et al. Infrastructure Complexity (2015) 2:5 Page 5 of 22 that eliminated serial correlation. These results were ignored. For the purposes of identifying the contribution of infrastructure to productivity growth, the parameters in the short-run equation were of relatively less interest as they did not account for the longer-term trends we were interested in. The coefficients from the long-run equation were the focus of the analysis. The short-run equation was of interest, principally, to indicate whether an individual country s per capita GDP growth did indeed revert to the long-run relationship identified. This was the case if the parameter on the error-correction term (ECM) was negative: other things being equal, aboveequilibrium output is met by lower growth in the following period and, conversely, below-equilibrium output was met by higher growth in the following period. The equations are estimated by Ordinary Least Squares (OLS) in lieu of others that may have better finitesample properties, but at the cost of reducing degrees of freedom; a concern owing to short time series in some cases. In addition to the basic regression of the form set out above, we also carried out a series of tests of robustness as discussed in Levine and Renelt (1992). These tests involved extensions to the basic specification with the addition of other explanatory variables, to assess the sensitivity of the results to alternative specifications. For comparability with the previous research we used the Eurostat equivalents of the following variables, which are among those thought to contribute to long-term productivity growth: h, a measure of human capital proxied by the proportion of adults who have completed an uppersecondary or tertiary education tax, the ratio of government tax receipts to GDP trade, trade openness, proxied by the ratio of the sum of imports and exports to GDP The sensitivity of the econometric results of the contribution of infrastructure to productivity growth can be gauged by the stability of the coefficient values following the addition of the above variables (one at a time, rather than en masse). We interpreted long-run coefficients on infrastructure that differed little as the equation specification changed as providing evidence of robustness. Insummary,thekeycriteriaweadoptedasindicative of a meaningful relationship between infrastructure and a country s productivity were: A statistically-significant parameter estimate for infrastructure (β 4 ) in the long-run (first-step) equation The presence of a cointegrating relationship in the long-run equation, as evidence of a well-specified equation Evidence of stability (robustness) in the estimated relationship, as judged by similar coefficient values in the additional equations Interpreting the equation results The parameter of interest in the analysis was that on infrastructure (β 4 ). It is this parameter that provided an indication of the contribution (or otherwise) of a particular infrastructure to a country s productivity. A key distinction between the original Mankiw et al. (1992) specification and the approach in this article is that the infrastructure investment in inf t is doublecounted in the total investment term s K t. This arises from the difference in measurement techniques: total investment is an economic volume while the infrastructure variable is in physical units. The conceptual problem was that corresponding physical data are not available for all other forms of capital, precluding a disaggregation such as that applied by Aschauer (1989). The advantage of using a physical indicator of infrastructure is that it provides a more accurate measure of that fixed capital compared to an economic-volume measure (as might be estimated by PIM, for example). A physical measure also overcomes problems of combining/reconciling public and private investment measures (as private financing has become increasingly relevant in many countries over time). Because disaggregation is not straightforward, we included both the total investment indicator and the infrastructure indicator in each regression. With the infrastructure indicator already included in economic terms in the investment indicator, the effect identified in such regressions should be interpreted as the contribution to productivity growth of infrastructure investment relative to investment in other forms of capital. A positive sign on the estimated coefficient indicated that investment in infrastructure was more efficient relative to other forms of investment. In that sense, a country may well be under-investing in its infrastructure for the purposes of raising productivity. Conversely, where the sign on an infrastructure coefficient was negative, this was interpreted as evidence of relative inefficiency in infrastructure investment, as such investment has relatively less effect in improving productivity. It is possible that such countries are overinvesting in such infrastructure, from the point of view of raising productivity. The assessment of the efficiency of infrastructure investment was considered in the light of the objective of raising productivity. It should be recognised that countries may

6 Thoung et al. Infrastructure Complexity (2015) 2:5 Page 6 of 22 have other objectives for wanting to increase their levels of investment in infrastructure and thus they may opt for non-optimal levels of infrastructure to balance their efforts with these other objectives. Data The focus of this article is on the contribution of infrastructure investment, relative to investment in fixed capital more generally, to productivity growth in Europe. The dataset for this analysis, sourced entirely from Eurostat, covers the 27 EU Member States (prior to Croatia s accession in 2013), Norway and Switzerland. Table 1 summarises the variables used in the regressions (see Appendix Table A for further information). The first four variables were included in all the regressions, along with one of the final five (the infrastructure variables, measured in physical units). These variables comprised the core equation specification. The analysis considered each of the infrastructure types in isolation i.e., there was one set of country-level equations for electricity, another set for rail etc. The analysis did not go on to model the combined contribution of these infrastructure types to productivity growth. As mentioned in the previous section, the analysis also considered the robustness of the estimates in the core equations by including additional control variables (numbered 5 7 in Table 1). These variables were included one at a time alongside the main five to test the sensitivity of the estimated contribution of infrastructure to productivity. The span of the data varies by country and infrastructure type, with the largest available samples (for which there are data for GDP per capita, investment, population and an infrastructure variable) covering , such that the dataset does include some periods from the recent recession. In the interests of maximising the length of the series, these years were preserved in the dataset. Where breaks were found within a series, the data points in the intervening years were linearly interpolated. The series that required most filling were the roadtransport variables: motorways and roads. For these variables, there were a number of missing periods between data points, generally before While a number of series are filled extensively before 1980 (usually over ), data limitations elsewhere actually meant that Denmark was the only country to make use of filled pre-1980 data (1975 onwards). Moreover, the results for this country did not yield a statistically-significant relationship from a well-specified cointegrating equation. A complete listing of filled data points can be found in Appendix Table B. Other than the aforementioned datafilling procedure, the only additional processing required was to aggregate series such as electricity capacity (which had to be aggregated up from the individual plant types) and telephones (the sum of fixed lines and mobile subscriptions) and derive per-capita series and ratios to GDP. The treatment of telephone lines attempted to account for the switch away from fixed lines towards mobile telephones, thus reflecting growth in connectivity (although, arguably, increases may represent the utilisation of the network, rather than increases in capacity). In this sense, of the five infrastructure types considered, telephones were perhaps the most at risk of actually signifying demand, rather than supply. The data on subscriptions was used in lieu of the availability of a more appropriate indicator (e.g., on the physical infrastructure, data for which tends to be proprietary, limiting its availability). Table 1 Regression variables Description Units 1 Y/L GDP per capita Millions of euros, 2005 chain-linked volumes per capita 2 s K Investment share % 3 N Population growth % 4 T Time trend 2005 = 0 5 H Human capital % of adults achieving an upper-secondary or tertiary education 6 Tax Ratio of tax receipts to GDP % 7 Trade Ratio of (exports + imports) to GDP % 8 Elec Electricity capacity per capita MW per capita 9 Mway Motorway length per capita km per capita 10 Rail Length of rail tracks per capita km per capita 11 Road Non-motorway length per capita km per capita 12 Tel Number of fixed-line and mobile telephone subscriptions per capita # lines/subscriptions per capita

7 Thoung et al. Infrastructure Complexity (2015) 2:5 Page 7 of 22 Some of the time series in the dataset were relatively short, with as few as 15 observations in some cases. The availability of data before then depended on the datatransmission procedures of the relevant national statistics office. By running single-country time-series regressions, we sought to use as much of the data as possible in each equation. Results and discussion This section presents the results from the analysis. It begins with a brief description of the preliminary analysis before providing an overview of the regression results. The remainder of this section goes on to discuss the results by individual infrastructure type, with a focus on their relative contribution to national productivity and whether there might be any evidence of over- or underinvestment with respect to the objective of raising productivity. Preliminary analysis The starting point was to consider the correlation matrix for the variables included in the long-run equation and examine the pair-wise relationships between the (natural logarithms of the) variables i.e., the variables as they appeared in the long-run equation (see Table A3 of the Appendix). With the exception of rail, the correlation between infrastructure and GDP was positive, with somewhat stronger positive correlation observed with electricity, motorway length and telephones. The correlation with road length was weaker while the correlation with rail was, negative, albeit weakly. Interestingly, the correlation between GDP per capita and the investment share was also mildly negative, as was the relationship between GDP per capita and education. The latter case may well be a result of a relatively short time series for education from the Eurostat database. The trade openness indicator exhibited a slightly negative correlation with GDP per capita while the relationship between the tax ratio and GDP per capita was quite strong. Unit root tests tended to fail to reject the null hypothesis of a unit root in the levels series (see Tables A4 and A5 of the Appendix for the results for GDP per capita and the investment share). There were higher rates of rejection in the first differences of the series although these results (particularly for GDP per capita) did not show strong evidence that the differenced data were stationary in all countries in the dataset. In the case of the infrastructure variables, null-hypothesis rejection rates on the differenced data were relatively low for telephones, electricity and rail (fewer than ten countries) but somewhat higher for roads and motorways (15 and 11 countries, respectively). This contrast with theory and other, previous empirical analyses may arise, at least in part, from the relatively short length of some of the time series and the low power of the Augmented Dickey-Fuller test. As an exploratory piece of analysis (and with further discussion of the merits of the approach in Section 6), the analysis in this article proceeded despite some series failing the unit-root tests, appealing to both theory and the aforementioned low power of the test. Overview of regression results Running the main regression model revealed that the mean long-run investment coefficients were in the range and broadly similar in size to those reported by Égert et al. (2009) of The coefficients on investment after including human capital were, in contrast to previous findings from the literature, higher than in the core regression, although many of the education indicators in our dataset have quite short time spans. Within the constraints of an analysis that draws on purely Eurostat data, this is a weakness of this particular equation. The investment coefficients were significant. The coefficients on population growth were not significant while the significance of the time trend varied across infrastructure types (it is significant for all but telephones) but was, in any case, small in size. The following sections consider the coefficients on the per-capita infrastructure variables, as it is these which indicate the contribution of each infrastructure type to productivity in each country (over and above the contribution of gross fixed capital formation, regardless of the type of capital). As discussed in the methodology, the main criteria by which we judged a relationship to be meaningful or valid from a statistical point of view were the statistical significance of the estimated coefficient (to distinguish, statistically, from a coefficient of zero, indicating no difference, in productivity terms, between additional infrastructure and additional conventional capital) and the presence of a cointegrating relationship between the variables in the long-run equation, guarding against the possibility of a so-called spurious regression from a mis-specified relationship. The additional equations tested the robustness of these relationships in terms of their stability on adding further variables to the specification. The tables on the following pages report the results from the econometric analysis. There is one table for each of the five infrastructure types considered (electricity, rail, road, motorways and telephones). In each table, there are four columns, one for each of the equations estimated: Main : the core equation specification, as set out in the methodology section

8 Thoung et al. Infrastructure Complexity (2015) 2:5 Page 8 of 22 Human capital : the core equation, with an additional variable to proxy human capital; in this case, the proportion of adults who have completed either an upper-secondary or tertiary education Tax : the core equation, with an additional variable indicating the size of government tax receipts as a ratio to GDP (to proxy the size of the government sector) Trade : the core equation, with an additional variable to capture a country s openness to trade (calculated as the ratio of the sum of exports and imports to GDP) Each column of each table reports: the mean coefficient on investment (investment as a share of output) from the long-run equation the mean coefficient on population growth from the long-run equation the mean coefficient on human capital (where applicable) from the long-run equation the mean coefficient on the time trend from the long-run equation the country-specific coefficients on the infrastructure variables (with indications as to whether the relationship is statistically significant, whether the long-run equation does in fact exhibit cointegration and the number of observations in the equation) the mean coefficient on the error-correction terms in the short-run equation the mean adjusted R 2 values of the long- and short-run equations the mean F-statistics of the long- and short-run equations Where we conclude that the results from the analysis suggest evidence of over- or under-investment, this is noted alongside the name of the country. Electricity For electricity, the longest time series available contained 22 observations, and the equations that yielded significant results generally had around 20 observations or more. The time series for other countries was shorter (closer to 15 observations) which may be a contributing factor in the lack of significance in these results. There are a number of positive coefficients on the electricity-capacity per capita term, but few of them satisfy the requirements of both statistical significance and cointegration in the long-run equation. In fact, of the basic equation specifications, only the relationship for Denmark satisfied the two criteria, suggesting that Denmark may benefit from further investment in electricity infrastructure (and is thus under-investing from the point of view of raising productivity). Even so, this result was not robust to the inclusion of human capital or the tax variable (becoming statistically insignificant), though it was robust in the trade variant of the equation. No other relationships in the basic specification were found to be positive and valid, although there are instances of such relationships in the variants to test for robustness. The results are summarised in Table 2. Evidence for over-investment in European electricitygeneration capacity (as judged by negative coefficient values) was somewhat stronger, particularly in Austria, Spain, Italy and the Netherlands. The results for Spain, Italy and the Netherlands were robust in at least two of the three alternative specifications (the result for Austria was only robust in the tax variant). Elsewhere, there were some valid negative relationships in the equations to test for robustness, but not the main equation. This included Belgium (tax and trade), Switzerland (trade only), France (trade only) Latvia (human capital only). Norway (human capital and tax) and Slovakia (human capital only). The evidence for over-investment in these countries was too weak to say that further investment is inefficient from a productivity point of view. However, in Germany, we found a valid positive relationship in the trade variant but a valid negative relationship in the tax variant: the results for this country were not robust. On balance, we found mild evidence of over-investment in electricity capacity in Europe and little evidence of under-investment. From these results, there was no particular reason to think that diverting investment towards electricity generation would contribute relatively more to productivity growth than investment in other assets. The objectives of a country are perhaps more complicated than the above analysis of this particular infrastructure from the point of view of productivity growth might suggest. This is because systemic electricitysupply under-provision has the potential to completely halt the economy in a way that a failure of, say, road infrastructure may not. In contrast to electricity infrastructure, a failure in road infrastructure would manifest itself as reduced service (congestion etc.). Hence, it will tend to be in a country s interest to invest in redundancy to ensure there is always adequate electricity provision. It is thus not necessarily the case that overinvestment in capacity, as is indicated in some Member States in the analysis above, is inefficient in a broader context, because there may be relatively less interest in optimal investment for productivity growth and relatively more interest in investment to promote resilience within the electricity system. Limited evidence of under-investment may support this idea of there being the need for a basic requirement of electricity provision in these economies.

10 Thoung et al. Infrastructure Complexity (2015) 2:5 Page 10 of 22 Moreover, because the power sector in Europe is a major emitter of greenhouse gases, one further goal of power-sector investment may be to reduce emissions, in line with legislated European targets for emissions reductions. In some countries, this would necessitate further investment, above that which might be considered optimal in productivity-growth terms. As an argument this appears reasonably intuitive: Member States must internalise (incur) the costs of emissions reduction in order to achieve their climate change mitigation targets. In this case, the Member States incur a cost in productivity-growth terms. Rail As with electricity the time series can be quite short for rail, with a number of equations having fewer than ten observations (in those cases, there is little point in reading much into the results). The results are summarised in Table 3. There are two countries that show positive relationships between infrastructure and output. The results for Norway are significant and satisfy our specification test of cointegration in all three robustness variants, but not the main specification (this requirement is met at the 15 % level, only). We also find a positive effect for Sweden, in the main equation and in the tax and trade variants (the coefficient from the human capitalaugmented equation was neither statistically significant nor indicative of a well-specified equation in terms of cointegration). The results suggest that productivity growth might be promoted through additional infrastructure investment. There are also positive relationships for Ireland and Latvia, although the former does not show statisticallysignificant results in the human capital or tax equations. The latter yields four significant results but three fail the cointegration test, leading to possibly spurious regressions. This is perhaps supported by the fact that the results for those three equations exceed 2.0 in value while the coefficient in the one equation that also satisfies the cointegration requirement is closer to 1.2 in value. The regression for France provides some evidence of a negative relationship, i.e., over-investment, in rail infrastructure. This result is robust to all but the trade variant of the specification. There is weaker evidence of over-investment for Austria, Italy and Poland, with the results only being significant and coming from a wellspecified equation in the robustness variants. Overall, the relationship between rail investment and productivity growth appears quite weak but this is likely to be related to the relatively short time series available from Eurostat. Road For road, there were positive relationships and thus evidence of possible under-investment for roads (excluding motorways) in Belgium, Ireland, the Netherlands and Slovenia. The results are summarised in Table 4. Of these, the results for Belgium and Ireland were significant and were part of cointegrating relationships in all four equations estimated. The remaining two were only robust to one variant: tax (for the Netherlands) and trade (Slovenia). We found weaker evidence for a positive relationship, albeit only in selected equation variants in Switzerland, Cyprus, the Czech Republic, Estonia, Spain, France, Norway and Portugal. Our analysis suggests that there are a small number of countries that may be over-investing in roads, as indicated by a negative coefficient on the infrastructure indicator. The strongest evidence of this is Austria, with more limited evidence for Latvia. Interestingly, we find two equations, for Lithuania, that satisfy our two criteria for a potentially-valid relationship, but for which the signs differ. Inspection of the other two equations in this set (the main equation and the trade alternative) support the negative relationship more than the positive but it is difficult to draw much from this because we are unable to establish the presence of cointegration in the longrun equation. Of the variables in our dataset, the series for roads and motorways were the ones subject to the most data filling. This was mostly to complete the series before 1980 although the limited availability of other data was a constraint in these regressions: only the equation for Denmark made use of the pre-1980 data, although after then there were some countries (notably the Netherlands), for which one or two data points at a time had to be filled. Overall, relatively few of the series actually made use of the filled data. Motorways As with roads, we found stronger evidence of positive relationships between motorways investment and productivity growth (suggestive of under-investment in these infrastructure assets). The results are summarised in Table 5. The evidence of positive relationships was particularly strong for Belgium, Cyprus, France and Italy. The results for Denmark were also positive, although the presence of cointegration could not always be established. Our results were not statistically significant for Austria, Spain and the Netherlands. Evidence of a negative relationship and potential under-investment was quite weak, with only Norway exhibiting more than one valid relationship across the four variants. Highly-significant results were evident in the equations with the longest time series (42 years of data). In the case of Belgium, our results suggested that

15 Thoung et al. Infrastructure Complexity (2015) 2:5 Page 15 of 22 investment in both roads and motorways would be beneficial for productivity growth. One could draw a similar, albeit weaker, conclusion for France, although the contribution of road was not quite as strong. Telephones For telephones (which we define as fixed-line and mobile subscriptions), we found a relatively large number of estimated relationships to be positive in nature for Austria, Belgium, Switzerland, Germany, Spain and Ireland, the Netherlands and Norway. Table 6 shows the results. Somewhat weaker evidence of a positive relationship was apparent in Lithuania, Luxembourg, Latvia, Portugal and Sweden. However, in some cases the span of the data was generally quite limited (15 years or less). As such, we did not read too much into these outcomes. Similarly, for the one country for which there might arguably be a negative relationship between telephone uptake and productivity growth, Malta, there were only ten observations and this hardly provided strong evidence of the estimated negative relationship. Moreover, only two of the four equations satisfied our criteria for a valid statistical relationship between productivity growth and infrastructure. The analysis presented in this article has applied a simple exogenous-growth model to analyse the contribution of infrastructure investment to the growth of productivity, over and above that of other noninfrastructure investment. In doing so, the approach allows for a comparable and consistent assessment of the contribution of infrastructure to a number of different European countries. Based as it is on an established theoretical and empirical framework, the analysis can be related to previous work both in the area of infrastructure economics but also the more-general field of economic growth. However, the analysis also carries some methodological limitations that relate to the specificities of infrastructure and the assumptions that underpin the chosen model. Investigating these limitations would be fruitful areas for future research and are discussed below. Infrastructure projects are typically large and costly. As such, and given that they often possess the characteristics of public goods, there has traditionally been an important role for the state in financing or guaranteeing such projects. This may in turn prompt questions as to the potential for state intervention (for example, if a country were to decide to pursue a renewed programme of investment to improve productivity) to crowd out private-sector investment. The source of finance is not considered in the analysis and the implicit assumption is that improvements in productivity from infrastructure investment are independent of the source of funding. Infrastructure is also distinct from many other forms of capital because of the manner in which it raises productive potential, by providing connectivity to other goods and services e.g., roads linking cities, enabling passenger and freight transport around a region. In many cases, infrastructure permits activity elsewhere whereas, for other forms of fixed capital, the asset permits a particular form of activity on-site. In that sense, location is important and, by extension, so is the likely differing quality of a particular infrastructure asset. As a result, aggregate, non-spatial measures of infrastructure may be misleading, by equating, say, the effect of one additional kilometre of road in one country with one additional kilometre in another. Moreover, such a treatment may, perhaps incorrectly, equate one additional kilometre with another in the same country (also raising the issue of economies of scale, discussed below). We have no explicit treatment of location or quality in this analysis and these limitations could be potentially addressed in future work. Such work might, for example, consider a set of infrastructure indicators (or even a composite one) that accounted for spatiality (e.g., proximity to areas of higher/lower output or population density); technology (e.g., electrified or non-electrified rail) or utilisation/congestion (e.g., in the case of roads or rail). A further assumption is that the infrastructure in place in a country only contributes to that particular country s productivity growth. In some countries, and for some infrastructure types, this may be true e.g., in the case of roads in island nations, where the connection boundary coincides with the national border. However, in other cases, this assumption is less tenable e.g., where there are electricity interconnectors between countries or, in mainland Europe, where roads and rail networks span multiple countries. The nature of infrastructure in such cases is that investment is mutually beneficial (and may be mutually financed), facilitating trade and other spillover effects. In an increasinglyconnected region such as Europe, developments in one country must take more account of impacts in other countries. Failing to account for this represents a potential source of bias in the results that would merit further investigation in the future. The equation specification, based as it is on per-capita measures, is also limited in its ability to deal with issues relating to economies of scale and the concentration/ density of production and population. Disaggregation or quality adjustment may well help in this area, too, as might other features of the countries geographical and economic structure (including with reference to adjacent countries).

16 Thoung et al. Infrastructure Complexity (2015) 2:5 Page 16 of 22 Finally, as Salimans (2012) points out, the application of a linear regression model derived from the framework of Mankiw et al. (1992) may be overly restrictive. This is because it restricts attention to models that comply with the classical Solow model. New growth theory puts forward an alternative class of models in which economic growth is a nonlinear function of its determinants. Moreover, Salimans (2012) emphasises the importance of joint analysis of variable selection and functional form (to test for such non-linearities). The analysis presented in this article addresses variable selection in the form of the robustness analysis of Levine and Renelt (1992) but not the functional-form issue, which may be highly relevant to infrastructure, which has a number of properties that distinguish it from many other forms of capital, such as its network/ connective features. While the current analysis permits comparisons to earlier work that adopts the neo-classical framework, comparisons against more-sophisticated analysis by Salimans (2012) and others would be an important area for investigation. The discussion above highlights various specificities relating to infrastructure that can complicate an analysis such as this one. However, these features also point to a number of interesting areas for future research. Some of these issues would require a more-extensive dataset and further work to develop an augmented version of the Eurostat-derived data would yield a number of advantages in the analysis of European economic growth. This is particularly because of the level of harmonisation required by Eurostat in the compilation of European statistics. Conclusions This article has identified the contribution infrastructure investment makes to productivity growth over and above that of investment in other, non-infrastructure forms of capital. We have followed an annual time-series regressions approach albeit with somewhat limited data in some cases but, where possible, using physical indicators of the size of infrastructure rather than the mainly expenditure-based measures used previously. We recognise that there is substantial heterogeneity in infrastructure effects across countries. In our analysis we found some evidence of over-investment in electricity generation capacity in Europe. We do, however, note that in the case of this infrastructure asset, resilient provision of infrastructure and/or transition to a low-carbon economy may take precedence. Productivity growth is but one objective in Europe, alongside considerations such as climatechange mitigation. Our analysis of rail found limited evidence of over or under-investment in this infrastructure type across countries while our results for roads and motorways provided stronger evidence that further investment in road-transport links might be beneficial for productivity growth. Similarly, we identified a number of countries for which the relationship between telephone connectivity and productivity growth was positive. There is no clear evidence in our results of differing effects between so-called Old and New Member States although in some cases the length of the time series can be quite short, making any kind of inference difficult. This is a limitation of our analysis and one of a number of areas that we would like to improve on in future research, in order to better identify the connective and spatial effects of infrastructure (e.g., at the city and region level). Endnotes 1 The consequent problem of not accounting for the public-private financing split is discussed later on in this article. 2 Égert, Kozluk and Sutherland (2009) note the difficulties in interpreting the coefficient on the infrastructure indicator as a result of the units by which it is measured (in physical terms) differing from the units by which capital accumulation is measured (in economic volumes). As such, it is the sign and the significance of the coefficients that is of primary interest 3 According to classical, rather than robust, standard errors. Appendix Table A1 lists the variables in the dataset used to carry out the regressions. All data are from Eurostat. An aggregate electricity capacity figure is not available in the Eurostat database and has instead been constructed as the following series (both main activity producers and auto producers) from the energy infrastructure database: Combustible fuels Nuclear Hydro Geothermal Wind Other sources Solar Tide, waves and ocean The final figures closely match the figures reported in Table of Eurostat (2012), which shows total installed capacity by broad technology. Note that these figures are total capacity, rather than net maximum capacity.

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